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Existence of Multiple Limit Cycles in a Predator-Prey Model with arctan(ax) as Functional Response

Commun. Math. Anal.
Volume 18, Number 1 (2015), 64 - 68

Existence of Multiple Limit Cycles in a Predator-Prey Model with arctan(ax) as Functional Response

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Abstract

We consider a Gause type predator-prey system with functional response given by $\theta(x)=\arctan(ax),$ where $a>0$, and give a counterexample to the criterion given in Attili and Mallak [Commun. Math. Anal. 1:33--40(2006)] for the nonexistence of limit cycles. When this criterion is satisfied, instead this system can have a locally asymptotically stable coexistence equilibrium surrounded by at least two limit cycles.